Advertisements
Advertisements
प्रश्न
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Advertisements
उत्तर
Let the points be A(a, b + c), B(b, c + a) and C(c, a + b)
Area of the triangle = `1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]`
= `1/2["a"("c" + "a") + "b"("a" + "b") + "c"("b" + "c") - "b"("b" + "c") + "c"("c" + "a") + "a"("a" + "b")]`
= `1/2["ac" + "a"^2 + "ab" + "b"^2 + "bc" + "c"^2 - ("b"^2 + "bc" + "c"^2 + "ac" + "a"^2 + "ab")]`
= `1/2 xx 0`
= 0
Since the area of a triangle is 0.
∴ The given points are collinear.
APPEARS IN
संबंधित प्रश्न
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
Find the area of triangle AGF
The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.
Find the area of an equilateral triangle whose perimeter is 180 cm
The area of the isosceles triangle is `5/4 sqrt(11)` cm2, if the perimeter is 11 cm and the base is 5 cm.
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?
Find the area of a parallelogram given in figure. Also find the length of the altitude from vertex A on the side DC.
A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
